| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2011 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Rotating disc with friction |
| Difficulty | Moderate -0.8 This is a straightforward application of circular motion with friction where F=μR provides centripetal force (mrω²). Part (a) requires one equation with standard substitution, parts (b)(i) and (b)(ii) are unit conversion and rearranging the same formula. All steps are routine M2 procedures with no problem-solving insight required. |
| Spec | 6.05b Circular motion: v=r*omega and a=v^2/r6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| For coin not to slide: friction provides centripetal force | M1 | Setting up equation |
| \(\mu mg \geq mr\omega^2\) | M1 | Correct equation |
| \(0.3 \times g \geq 0.8\omega^2\) | A1 | Substituting values |
| \(\omega \leq \sqrt{\frac{0.3g}{0.8}} = 1.92\) rad s\(^{-1}\) | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| \(\omega = 45 \times \frac{2\pi}{60}\) | M1 | Converting rpm to rad/s |
| \(\omega = \frac{3\pi}{2} = 4.71\) rad s\(^{-1}\) | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| \(\mu mg \geq mr\omega^2\) | M1 | Setting up inequality |
| \(\mu \geq \frac{r\omega^2}{g} = \frac{0.15 \times \left(\frac{3\pi}{2}\right)^2}{g}\) | M1 A1 | Substituting values |
| \(\mu \geq \frac{0.15 \times \frac{9\pi^2}{4}}{9.8} = 0.337\) | A1 | cao |
# Question 5(a):
| Working/Answer | Mark | Guidance |
|---|---|---|
| For coin not to slide: friction provides centripetal force | M1 | Setting up equation |
| $\mu mg \geq mr\omega^2$ | M1 | Correct equation |
| $0.3 \times g \geq 0.8\omega^2$ | A1 | Substituting values |
| $\omega \leq \sqrt{\frac{0.3g}{0.8}} = 1.92$ rad s$^{-1}$ | A1 | cao |
# Question 5(b)(i):
| Working/Answer | Mark | Guidance |
|---|---|---|
| $\omega = 45 \times \frac{2\pi}{60}$ | M1 | Converting rpm to rad/s |
| $\omega = \frac{3\pi}{2} = 4.71$ rad s$^{-1}$ | A1 | cao |
# Question 5(b)(ii):
| Working/Answer | Mark | Guidance |
|---|---|---|
| $\mu mg \geq mr\omega^2$ | M1 | Setting up inequality |
| $\mu \geq \frac{r\omega^2}{g} = \frac{0.15 \times \left(\frac{3\pi}{2}\right)^2}{g}$ | M1 A1 | Substituting values |
| $\mu \geq \frac{0.15 \times \frac{9\pi^2}{4}}{9.8} = 0.337$ | A1 | cao |5
\begin{enumerate}[label=(\alph*)]
\item A shiny coin is on a rough horizontal turntable at a distance 0.8 m from its centre. The turntable rotates at a constant angular speed. The coefficient of friction between the shiny coin and the turntable is 0.3 .
Find the maximum angular speed, in radians per second, at which the turntable can rotate if the shiny coin is not going to slide.
\item The turntable is stopped and the shiny coin is removed. An old coin is placed on the turntable at a distance 0.15 m from its centre. The turntable is made to rotate at a constant angular speed of 45 revolutions per minute.
\begin{enumerate}[label=(\roman*)]
\item Find the angular speed of the turntable in radians per second.
\item The old coin remains in the same position on the turntable.
Find the least value of the coefficient of friction between the old coin and the turntable needed to prevent the old coin from sliding.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA M2 2011 Q5 [10]}}